Agent Rogelio Martinez, 36, died Sunday after he and his Big Bend sector partner responded to "activity near Interstate 10" in the Van Horn area, which is about 120 miles east of El Paso.
His partner, whose name hasn't been released, had reported that they were injured and needed assistance, according to U.S. Customs and Border Protection.
Martinez's partner was in stable condition Monday in the intensive care unit of an El Paso hospital.
“We owe a great deal of gratitude to the brave men and women of the United States Border Patrol who serve every day to protect our homeland,” Texas Gov. Greg Abbott said in a statement announcing the reward from the state's Crime Stoppers program.
“As authorities continue their investigation, it is important that they receive any and all information to help apprehend and deliver swift justice to those responsible.”
Few details have been released by authorities who said the incident is still under investigation.
The FBI in a news release Monday night said Border Patrol agents from the Van Horn station found the two agents “in a culvert area” adjacent to I-10 about 12 miles east of Van Horn late Saturday night. They provided immediate medical care and took them to a Van Horn hospital.
The agents sustained traumatic head injuries and broken bones, according to the FBI.
Their injuries were determined to be severe, which required advanced medical care, so the agents were airlifted to an El Paso hospital, the agency said.
"Whenever the FBI suspects a member of the federal law enforcement community has been the victim of a violent assault, the FBI is responsible for investigating the matter," FBI officials said in the statement.
National union leaders initially told media that the agents had been hit with rocks but, on Monday, representatives issued a statement that did not reflect those comments. The information also has not been confirmed by the FBI.
"The cause of this tragedy is not being reported as this situation is unfolding and an active investigation is underway," national union officials said in a statement. "Various local and federal authorities are on scene to assist with the investigation and to search the area for any suspects or witnesses."
Stu Harris, vice president of the National Border Patrol Council Local 1929 in El Paso, said the agents were attacked, but could not confirm whether they had been hit with rocks.
"Right now, we are focusing on making sure the families are being taken care of," Harris said. "We are letting the investigation take place and seeing if they can bring these people to justice."
Martinez had been a Border Patrol agent since August 2013, a spokesman said.
According to statistics, attacks on U.S. Border Patrol agents and U.S. Customs and Border Protection officers grew in the 2017 fiscal year.
About 671 Border Patrol agents were attacked in 2017, a 67% increase from the previous year when 403 agents were assaulted.
Altogether, there were 720 assaults on Border Patrol agents and CBP officers during the 2017 fiscal year, compared with about 585 in 2016.
President Trump on Sunday reiterated his calls for a border wall in a tweet about the incident.
"Border Patrol Officer killed at Southern Border, another badly hurt. We will seek out and bring to justice those responsible. We will, and must, build the Wall!"
U.S. Rep. Will Hurd, a Republican whose district stretches from El Paso County to San Antonio, said his thoughts and prayers are with Martinez's family and his injured partner. He said the two served their country by protecting the border.
"The men and women of our Border Patrol have an incredibly dangerous and demanding job and they are our most important resource to securing our border," Hurd tweeted Sunday.
In a statement, U.S. Sen. Ted Cruz, R-Texas, said the two agents had been attacked.
“This is a stark reminder of the ongoing threat that an unsecure border poses to the safety of our communities and those charged with defending them," Cruz said. "We are grateful for the courage and sacrifice of our border agents who have dedicated their lives to keeping us safe."
U.S. Rep. Beto O'Rourke, D-El Paso, wrote on Twitter: "My thoughts are with the family of agent Rogelio Martinez & the entire Border Patrol. We will pursue investigation & justice."
Texas Attorney General Ken Paxton called Martinez a hero.
“I wish to extend my deepest condolences to the family of Agent Rogelio Martinez killed in the line of duty yesterday in Texas," Paxton said in a statement Monday. "He served our country faithfully and will forever be remembered as a heroic officer."
The FBI, the Culberson County Sheriff’s Department, the Office of the Inspector General and CBP’s Office of Professional Responsibility are investigating the incident.
“Our thoughts and prayers are with Agent Martinez and his family and with the agent who was injured,” CBP officials said in a statement.
How to report information
Anyone with information on the incident may anonymously call Crime Stoppers of Texas.
By phone: 1-800-252-8477
By text: Send a text message to 274637 by entering the word "DPS" (include the quote marks)
Online: Visit the Texas Department of Public Safety's tips website at dps.texas.gov.